FeCo thin films were prepared on SrTiO3(100), SrTiO3(110), and SrTiO3(111) single-crystal substrates by ultra-high vacuum molecular beam epitaxy. The film growth structure and magnetic properties were investigated. FeCo epitaxial thin films are obtained on these SrTiO3 substrates at elevated temperatures with different crystal growth orientations. The nucleation and growth process of FeCo thin films on SrTiO3 substrates vary depending on the orientation of the substrate and its temperature. FeCo(100) single-crystal thin films with an A2 structure are obtained on SrTiO3(100) substrates at 500°C. FeCo epitaxial thin films with (110)A2 and (211)A2 planes parallel to the substrate surface are obtained on SrTiO3(110) substrates. FeCo thin films epitaxially grown on SrTiO3(111) substrates consist of two crystallographic phases having A2 and hexagonal structures with the (110)A2 and (0001)hex planes parallel to the substrate surface. The metastable FeCo(0001)hex plane is presumably formed in order to relax the strain caused by the lattice mismatch at the FeCo/SrTiO3(111) interface. The lattice constants of Fe50Co50 crystal with the hexagonal structure are estimated to be a = 0.251±0.004 nm and c = 0.457±0.005 nm. The magnetic properties of FeCo epitaxial thin films grown on SrTiO3 substrates are influenced by the magnetocrystalline anisotropy and shape anisotropy caused by the roughness of FeCo islands that form the FeCo thin films.